caa a22 4500 605523789 CHVBK 20210128100751.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10958-015-2570-7 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2570-7 The Behavior of Solutions to the Dirichlet Problem for Second Order Elliptic Equations with Variable Nonlinearity Exponent in a Neighborhood of a Conical Boundary Point [Elektronische Daten] [Yu. Alkhutov, M. Borsuk] We study the Dirichlet problem for the p-Laplacian in a conical domain with the homogeneous boundary condition on the lateral surface of a cone with vertex at the origin. We assume that the variable exponent p = p(x) is separated from 1 and ∞ and denote by Ω the intersection of the cone with the unit (n − 1)-dimensional sphere. We prove that (i) if p satisfies the Lipschitz condition and ∂Ω is of class C 2+β, then the solution to the Dirichlet problem is O(|x| λ ) in a neighborhood of the origin, where λ is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the p(0)-Laplacian and (ii) if p satisfies the Hölder condition, p(0) = 2, and ∂Ω is of class C 1+β, then the solution to the Dirichlet problem is O(|x| λ0) in a neighborhood of the origin, where λ 0 is the sharp exponent of tending to zero of solutions to the same Dirichlet problem for the Laplace operator. Bibliography: 18 titles. Springer Science+Business Media New York, 2015 Alkhutov Yu A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia aut Borsuk M. University of Warmia and Mazury, 2, Michala Oczapowskiego St., Olsztyn, Poland aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 341-370 1072-3374 210:4<341 2015 210 10958 https://doi.org/10.1007/s10958-015-2570-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2570-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alkhutov Yu A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia aut NATIONALLICENCE 700 1- Borsuk M. University of Warmia and Mazury, 2, Michala Oczapowskiego St., Olsztyn, Poland aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/4(2015-10-01), 341-370 1072-3374 210:4<341 2015 210 10958